Math, asked by himanshin1608, 1 year ago

if 5,a2,a3,.......,a20,145 is an a.p.,Then a2+a20

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Answered by satyarth42
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nareshbyagari4989

20.07.2018

Math

Secondary School

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If a1,a2,a3,..........are in ap such that a1+a5+a10+a15+a20+a24=225, then a1+a2+a3+..........a23+a24 is

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a1 + a5 + a10 +a15 + a20 + a24 = 225 (given)

(a1+a24) + (a5+a20) + (a10+a15) = 225 .................1

let first term is a & common difference is d then

a1 = a , a24 = a+23d , a1+a24 = 2a+23d ..........2

a5 = a+4d , a20 = a+19d , a5+a20 = 2a+23d ..............3

a10 = a+9d , a15 = a+14d , a10+a15 = 2a+23d ..............4

putting 2 , 3 , 4 in eq 1 we get

3(2a+23d) = 225

2a+23d = 75 ...........5

now , a1 + a2 + a3 ............a24 = S24

S24 = 24/2[2a+(24-10d)]

=12(2a+23d) ...............6

from 5 & 6

S24 = 12*75 = 900

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